I believe it is an Americanism. As krillco says the origins may be Yiddish.
Jews from Germany and Central Europe arriving in New York at the end of the 19th Century brought Yiddish from their homelands, shm is a fairly common prefix in Yiddish and their culture relys on a great deal of argument over the correct interpretation of matters .
New Yorkers hearing the rhythm of Yiddish debators picked up on the sound of the language and played with the tones. The habit also spread into Vaudeville comedy acts and spread around the country. This accepted form of vocabulary then entered the world of the movies and became a recognized play on words meant to show disagreement.